Lemma 12 (Lemma 3.7, [1]}) 

Given a locally Lipschitz definable function \(f\)  with an open domain \(D\subset \lbrace x|\Vert x\Vert >1\rbrace \) , for any \(\lambda >0\) , there exists \(a>0\) , and a definable desingularizing function \(\Psi \)  on \([0,a)\)  such that
\(\max \left\lbrace 1, \frac{2}{\lambda }\right\rbrace  \Psi ^{\prime }(f(x))\Vert x\Vert ^{1+\lambda }\Vert \bar{\partial } f(x)\Vert  \ge 1, \text{ if } f(x)\in (0,a).\) 

